Profit And Loss
Math MCQs

Question :    Mr. John sold his scoory for $1465.10 and got a loss of 9%. What was the cost price of the scooty?

Correct Answer  $1610

Solution & Explanation

Solution

Finding the cost price if the sale price and loss percent are known

The cost price (CP) can be found using the formula, algebraic method, shortcut method, and taking the cost price as 100, 200, 300, 400, 500, or whatever you want. Here the five methods to solve this problem have been given.

Method (1) Using Formula

Finding the cost price using the formula when the sale price and loss percent are known

Given, the sale price (SP) = $1465.1

And, the loss = 9%

Then, the Cost Price (CP) = ?

Formula to find the cost price when the sale price and loss percent are known

Cost Price (CP) = ¹⁰⁰/_{100 – gain%} × SP

Thus, the Cost Price (CP)

= ¹⁰⁰/_{100 – 9} × 1465.1

= ¹⁰⁰/₉₁ × 1465.1

= ¹⁴⁶⁵¹⁰/₉₁ = 1610

Thus, the Cost Price (CP) = $1610 Answer

Method (2) Algebraic Method

Finding the cost price (CP) using the Algebraic Method when the Sale Price (SP) and the loss percent are given

Let the Cost Price (CP) = m

Here given loss = 9%

Calculation of loss

The loss and/or profit is calculated on the cost price (CP)

Formula to find the loss when the Cost Price and the Loss% are given

Loss = loss% of CP

Thus, loss on the cost price of m

= Loss% of m

= 9% of m

= 9% × m

= ²/₁₀₀ × m

⇒ loss = ^{9 m}/₁₀₀

Calculation of Cost Price (CP)

Formula to find the Sale Price (SP) when the Cost Price (CP) and the Loss are given

Sale Price (SP) = Cost Price (CP) – Loss

⇒ 1465.1 = m – ^{9 m}/₁₀₀

⇒ 1465.1 = ^{100 m – 9 m}/₁₀₀

⇒ 1465.1 = ^{91 m}/₁₀₀

After cross multiplication, we get

1465.1 × 100 = 91 m

⇒ 91 m = 1465.1 × 100

⇒ m = ^{1465.1 × 100}/₉₁

⇒ m = ^{1465.1 × 100}/₉₁

⇒ m = ¹⁴⁶⁵¹⁰/₉₁ = 1610

Thus, the Cost Price (CP) = $1610 Answer

Method (3) Unitary Method

Finding the cost price (CP) using Unitary Method by taking the cost price (CP) is equal to 100 when the SP and the loss percent are given

Given, the sale price (SP) = $1465.1

And, the loss = 9%

Then, the Cost Price (CP) = ?

Let Cost Price (CP) = 100

Thus loss = 9% of 100 = 9

Thus, Sale Price (SP) = Cost Price (CP) – loss

⇒ Sale Price (SP) = 100 – 9

⇒ Sale Price (SP) = 91

∵ If the Sale Price (SP) is 91, then the Cost Price (CP) = 100

∴ If the Sale Price (SP) is 1, then the Cost Price (CP)

= ¹⁰⁰/₉₁

∴ If the Sale Price (SP) is 1465.1, then the Cost Price (CP)

= ¹⁰⁰/₉₁ × 1465.1

= ^{100 × 1465.1}/₉₁ = 1610

Thus, the Cost Price (CP) = $1610 Answer

Method (4) Shortcut Method (1)

Shortcut Method to find Cost Price (CP) when SP and loss percent are known

Given, the sale price (SP) = $1465.1

And, the loss = 9%

Then, the Cost Price (CP) = ?

SP = 91% of CP

⇒ SP = 91% of CP

⇒ 1465.1 = ⁹¹/₁₀₀ × CP

⇒ 1465.1 = ^{91 CP}/₁₀₀

After cross multiplication

⇒ 1465.1 × 100 = 91 CP

⇒ 91 CP = 1465.1 × 100

⇒ CP = ^{1465.1 × 100}/₉₁

⇒ CP = ¹⁴⁶⁵¹⁰/₉₁ = 1610

⇒ CP = $1610 Answer

Method (5) Shortcut Method (2)

Shortcut Method (2) to find Cost Price (CP) when SP and loss percent are known

Here loss and the Sale Price are given and the Cost Price is to find

Here as given, the loss = 9%

And the Sale Price = $1465.1

This means 100 – loss% of the Cost Price = Sale Price

⇒ 100 – 9% of the Cost Price = $1465.1

⇒ 91% of the Cost Price = 1465.1

Therefore, 1% of the Cost Price = ^1465.1/₉₁

Thus, 100% the Cost Price = ^1465.1/₉₁ × 100

= ¹⁴⁶⁵¹⁰/₉₁ = 1610

Thus the Cost Price (CP) = $1610 Answer

Similar Questions

(1) Mrs. Julie purchased 26 oranges for $1 and sold 25 oranges for $1. What will be his profit percentage??

(2) John loses 64% by selling an article for $1101.60. For how much should he sell it to get a profit of 63%?

(3) After selling an article for $1565.5 the shopkeeper earns a profit of 55%. For how much had he purchase that article?

(4) James loses 67% by selling an article for $1059.30. For how much should he sell it to get a profit of 66%?

(5) A trader earns a profit of 170% by selling an article for $8937. Find the cost price.

(6) A dealer earns a profit of 285% by selling some items for $21598.50. What was his cost price?

(7) How much percent will Peter earn if he buys 37 articles for $1 and sells 36 articles for $1?

(8) After selling some items for $6884.50 Mr. Bob earns 145%. Find the cost price of those items.

(9) If Mrs. Julie earned a profit of 335% by selling her car for $28753.50 then, what was the cost price of the car?

(10) If a trader gets a loss of 13% by selling some colthes for $2096.70 then find the cost price.